Piecewise Functions From real World Problems

Today’s objective:

I can write a piecewise function from

multiple representations.

(From a Real World Scenario)

CREATING
PIECEWISE

FUNCTIONS FROM

REAL WORLD

SCENARIOS – DAY

3

Multiple Choice

Find f(-2)

• -3

• 6

• 8

• -6

4-Step Problem Solving Process:

STEP 1: Understand the problem:

a) Read the entire problem.

b) Can you restate the problem?

Multiple Choice

Match the graph with the correct equation.

4-Step Problem Solving Process:

STEP 2: Devise a Plan:

a) Highlight any given information.

b) Eliminate any unnecessary info.

c) Define the variable using the

unknown info.

d) Relate the given info to the unknown

info with a formula or equation.

4-Step Problem Solving Process:

STEP 3: Execute the Plan:

a) Model the problem with the equation.

b) Solve the equation for the unknown.

c) Be sure to label the units.

4-Step Problem Solving Process:

STEP 4: Check Your Work:

a) Check the solution in the original

equation.

b) Does your answer make sense in the

context of the problem?

Example 1: Create a Piecewise Function

You go to Wal-Mart to buy some candy. You
decide to buy snickers because they have
a special deal on snickers. A bag of snickers
costs $3.45, but if you buy 4 or more bags,
they only cost $3.00per bag.

Create a piecewise function to represent the
cost of the bags of snickers.

Solution: Example 1
•b = number of bags of snickers
•C(b) = Cost of all bags of snickers purchased
•$3.45 = cost of a bag if less than 4 bags are
purchased
•$3.00 = cost of a bag if 4 or more bags are
purchased.

Multiple Choice

• $12.75

• $35

• $45

• $27.75

Example 2: Create a Piecewise Function

The Mad Hatter is ordering cups from Teacups,
Limited, for his tea party. The Teacups, Limited
catalog prices cups according to the number of
cups ordered. For orders of 20 or fewer cups,
the price is $1.40 per cup plus $12 shipping and
handling on the order. For orders of more than
20 cups, the price is $1.10 per cup plus $15
shipping and handling.

a)
Create a function to describe the price of

cups.

Example 2: Create a Piecewise Function

b) How much will it cost the Mad Hatter to
order 16 cups?

c) If the Mad Hatter wants to spend at most
$45, what is the maximum number of cups he
can order?

Solution: Example 2
•c = the number of cups ordered
•P(c) = the price of all cups ordered
•$1.40 cost of each cup if 20 or less are ordered
•$12.00 shipping if 20 or less are ordered
•$1.10 cost of each cup if more than 20 are ordered
•$15.00 shipping if more than 20 are ordered

b) $34.40

c) 27 cups

Example 3: Create a Piecewise Function

Every month your cell phone plan costs $75
and gives you unlimited talk, 500 text
messages, and no data plan. It costs $0.10
per text message sent in excess of the 500
that you are originally allotted.

a) Write a piecewise function to determine
the amount of your cell phone bill.

b) How much will it cost you if you send 750
text messages?

Solution: Example 3
•$75 = monthly cost of cell phone bill
•$0.10 = cost of each text in excess of the plan’s
allotted 500.
•t = number of text messages sent
•T-500 = number of texts in excess of 500 allotted
•C(t) = Cost of your cell phone bill

b) $100

Example 4: Create a Piecewise Function

A construction worker earns $17 per hour for
the first 40 hours of work and $25.50 per
hour for work in excess of 40 hours.

a) Create a function to represent the amount

of her paycheck.

b) One week she earned $896.75. How much
overtime did she work?

Solution: Example 4
•$17 = hourly pay: hours up to 40.
•$25.50 = hourly pay; hours in excess of 40
•h = # of hours worked
•h-40 =# hours worked in excess of 40
•P(h) = total amount of paycheck

b) 8.5 overtime hours

Example 5: Create a Piecewise Function

Southeast Electric charges $0.09 per
kilowatt-hour for the first 200 kWh. The
company charges $0.11 per kilowatt-hour for
all electrical usage in excess of 200 kWh.

a) Create a function to model this scenario.

b) How many kilowatt-hours were used if a
monthly electric bill was $57.06?

Solution: Example 5

•h = # kilowatt-hours
•C(h) = Cost of total kilowatt-hours

b) 555.09 Kwh

Multiple Choice

A house painter charges $12 per hour for the first 40 hours he works, $18 for the ten hours after that, and $24 for all hours after that.

How much does he earn for a 70 hour week?

• $1020

• $1140

• $840

• He works for free!

YOU TRY: On Your Whiteboard!
Ex. 1: A city parking lot uses the following
rules to calculate parking fees:
1. A flat rate of $5.00 for any amount of time

up to and including the first hour.

2. A flat rate of $12.50 for any amount of

time over 1 hour and up to and including 2
hours.

3. A flat rate of $13 plus $3 per hour for each

hour after 2 hours.
Create a piecewise function to model the

parking fees.

YOU TRY: On Your Whiteboard!

Ex. 2: Your job pays you $8.50 an hour for a
normal 40 hour work week. If you work over
40 hours then you get paid overtime, at
time and half (1.5 times your normal rate)
for anything over 40 hours, but you are not
allowed to work more than 20 overtime
hours.
a) Create a function that models this

scenario.

b) How much would your paycheck be if you

worked 45 hours?

YOU TRY: On Your Whiteboard!

Ex. 3: Every month your cell phone plan
costs $230 and gives you unlimited talk,
text messages, and 2GB of data. Extra
data for each month is $15 per GB you go
over your allotted 2GB.

a)Write a piecewise function to represent
this situation.

YOU TRY: On Your Whiteboard!
Ex. 4: You are teaching tomorrow with an
activity and you want to use candy to
motivate your students. You go to Fred’s
Food Club and they have a special going on
for blow pops. For 2 or less bags it cost
$4.35 for each bag, but if you buy more
than 2 bags you get the special price of
$3.25 per bag.

a) Write a piecewise function to represent
this situation.

Multiple Choice

• $12.75

• $35

• $43.40

• $27.75